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Determine the maximum speed that the cars of the roller coaster can reach along the circular portion AB of the track if \( p \) is 25 m and the normal component of their acceleration cannot exceed \( 3g \).

Select one:

A. \( V_{\text{max}} = 97.6 \) km/h
B. \( V_{\text{max}} = 100 \) km/h
C. \( V_{\text{max}} = 97.6 \) m/h

Answer :

The maximum speed that the cars of the roller-coaster can reach along the circular portion AB of the track is approximately 97.6 km/h.

To determine the maximum speed that the cars of the roller-coaster can reach along the circular portion AB of the track, we can use the centripetal acceleration formula and the given information.

The centripetal acceleration (a) is given by the equation:where v is the velocity and r is the radius of the circular portion AB of the track.

We are given that the normal component of the acceleration cannot exceed 3g, where g is the acceleration due to gravity.

The normal component of the acceleration (an) is given by:

To convert the normal component of the acceleration to g, we divide by the acceleration due to gravity:

Rearranging the equation, we have:

v^2 = 3g * r.

Now, we can substitute the given values:

g = 9.8 m/s^2 (acceleration due to gravity),

r = 25 m (radius of the circular portion AB).

v^2 = 3 * 9.8 * 25.

v^2 = 735.

Taking the square root of both sides, we find:

v = 735

​Calculating the value, we get:

v ≈ 27.1 m/s.

To convert this to km/h:

v ≈ 27.1 * 3.6 ≈ 97.6 km/h.

So the correct answer is a. Vmax = 97.6 km/h.

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